Finite Group DatabasebetaFinite Group Databasebeta| order | 6370 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D637 |
| unambiguous semidirect product | C13⋊(C5×D49) |
| unambiguous semidirect product | C49⋊(C5×D13) |
| Fitting, Hall | C5×C13×C49 ⋊ C2 |
| derived, Hall | C13×C49 ⋊ C2×C5 |
| Hall | C5×C49 ⋊ D13 |
| Hall | C5×C13 ⋊ D49 |
| Sylow | C49 ⋊ C5×D13 |
| Sylow | C13 ⋊ C5×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D637 |
| commutator, hypocenter | C13×C49 | C2×C5 |
| Frattini | C7 | C5×D91 |
| Fitting | C5×C13×C49 | C2 |
| socle | C5×C7×C13 | D7 |
| LCS | G ▷ C13×C49 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
1600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D13×D49, D5×D637, D65⋊D49, … |
| maximal normal subgroup of | C5×D13×D49, D5×D637, D65⋊D49, … |
| maximal quotient of | C5×Dic637, C2×C5×D637, C3×C5×D637, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6370, 4);